AC Circuits: Phasors/Polar to rectangular transformation

[sgonzalez90]

40<50degrees + 20<-30 degrees,
I get how to convert to rectangular,

I got 43.03 + j20.64, but converting it back to polar... how exactly do you do so? The answer is 47.72<25.63degrees... my book doesn't explain it.

Also with
(2+j4)(3-j5)... how exactly do you tackle this sort of problem? I tried the FOIL method and it didn't exactly work.


Thank you!

 

[sgonzalez90]

Homework Statement

40<50degrees + 20<-30 degrees,
I get how to convert to rectangular,

I got 43.03 + j20.64, but converting it back to polar... how exactly do you do so? The answer is 47.72<25.63degrees... my book doesn't explain it.

Also with
(2+j4)(3-j5)... how exactly do you tackle this sort of problem? I tried the FOIL method and it didn't exactly work.


Thank you!

 

[SirAskalot]

Length: |I|= sqrt(Re²+Im²)

sqrt(43²+21²)=48

Angle: < = arctan (Im/Re)

arctan (21/43) = 26 (deg)

Draw a phasor diagram and you see it easily. Simple geo/trig.

Part 2:
Either convert to polar form and multiply the length and add the angles, or just multiply out the two parenthesis inn a normal fashion. Remember j*j=-1

 

[Zryn]

Rectangular $$\rightarrow$$ Polar

x + jy $$\rightarrow$$ $$\sqrt{x^{2} + y^{2}}$$ $$\angle$$ $$tan^{-1}(\frac{y}{x})$$

There are a lot of calculators which can do this for you too!


(2+j4)(3-j5) ... FOIL is the way, expand the brackets first

2*3 + 2*-j5 + j4*3 + j4*-j5 ... simplify

6 - 10j + 12j - 20j*j ... keep in mind j = $$\sqrt{-1}$$, so $$j^{2}$$ = -1

6 +2j + 20

26 + 2j

 

[DeeNos]

I am happy to provide a response to your questions about AC circuits and phasors. The conversion from polar to rectangular coordinates is a common technique used in electrical engineering to simplify calculations and analysis of AC circuits. In order to convert back to polar coordinates, you can use the following formula:

Magnitude = √(real^2 + imaginary^2)
Angle = tan^-1(imaginary/real)

In the example you provided, the magnitude would be √(43.03^2 + 20.64^2) = 47.72 and the angle would be tan^-1(20.64/43.03) = 25.63 degrees.

As for the problem with (2+j4)(3-j5), you can use the FOIL method to multiply the two complex numbers. This would result in a final answer of 26 + j2.

I hope this helps clarify the concepts for you. Remember, practice makes perfect and don't hesitate to ask for help or consult other resources if you are still struggling with these concepts. Good luck!